| dc.contributor.advisor | Yıldırım, Hüseyin | |
| dc.contributor.author | Özkan, Umut Mutlu | |
| dc.date.accessioned | 2019-05-28T12:36:49Z | |
| dc.date.available | 2019-05-28T12:36:49Z | |
| dc.date.issued | 2007 | |
| dc.identifier.uri | http://hdl.handle.net/11630/6236 | |
| dc.description | In this study we obtained Hardy-Knopp-type integral inequality
b
a
u(x)
1
(x) a
(x)
f(t) t
a
x
x a
b
a
v(x) (f (x))
x
x a
and two-dimensional Hardy-Knopp-type integral inequality
b d (x) (y)
1 1x 2y
f(t;s) 1t 2s
( (x) a)( (y) c) (x a)(y c)
a c a c
b d
t a s c 1t 2s
(f (t;s)) 1 1
b a d c (t a)(s c)
a c
on time scales. Then we stated and proved that Hardy integral inequality involving several functions on time scales.
In the last part we study Young’s inequality, Hölder’s inequality, Minkowski’s inequality and Jensen’s inequality …rst using nabla integral and later diamond-
integral on time scales. Consequently we obtained new generalizations of Young, Hölder, Minkowski and Jensen inequalities using -derivative on time
scales. | en_US |
| dc.description.abstract | Bu çal¬¸smada, zaman skalas¬nda
b
a
u(x)
1
(x) a
(x)
f(t) t
a
x
x a
b
a
v(x) (f (x))
x
x a
¸seklindeki Hardy-Knopp tipli integral e¸sitsizli¼gi ve
b d (x) (y)
1 1x 2y
f(t;s) 1t 2s
( (x) a)( (y) c) (x a)(y c)
a c a c
b d
t a s c 1t 2s
(f (t;s)) 1 1
b a d c (t a)(s c)
a c
¸seklindeki 2-boyutlu Hardy-Knopp tipli integral e¸sitsizli¼gi elde edilmi¸stir. Daha sonra zaman skalas¬nda birden fazla fonksiyon içeren Hardy integral e¸sitsizli¼gi ifade ve ispat edilmi¸stir.
Son bölümde, zaman skalas¬nda Young, Hölder, Minkowski ve Jensen e¸sit-
sizlikleri ilk olarak r-türev, daha sonra -türev kullan¬larak elde edilmi¸stir.
Dolay¬s¬yla -türev kullanarak elde edilen Young, Hölder, Minkowski ve Jensen
e¸sitsizlikleri zaman skalas¬nda yeni genelle¸stirmelerdir. | en_US |
| dc.language.iso | tur | en_US |
| dc.rights | info:eu-repo/semantics/openAccess | en_US |
| dc.subject | Delta türev, Nabla türev, Diamond- di- namik türev, Hardy integral e¸sitsizli¼gi, Dinamik e¸sitsizlik ve Zaman skalas¬. | en_US |
| dc.title | Zaman Skalasinda·Integral Esitsizlikleri | en_US |
| dc.title.alternative | Integral Inequalities And Its Applications On Time Scales | en_US |
| dc.type | masterThesis | en_US |
| dc.department | Fen Bilimleri Enstitüsü | en_US |
| dc.identifier.startpage | 1 | en_US |
| dc.identifier.endpage | 50 | en_US |
| dc.relation.publicationcategory | Tez | en_US |
